

A154747


Decimal expansion of sqrt(sqrt(2)  1), the radius vector of the point of bisection of the arc of the unit lemniscate (x^2 + y^2)^2 = x^2  y^2 in the first quadrant.


7



6, 4, 3, 5, 9, 4, 2, 5, 2, 9, 0, 5, 5, 8, 2, 6, 2, 4, 7, 3, 5, 4, 4, 3, 4, 3, 7, 4, 1, 8, 2, 0, 9, 8, 0, 8, 9, 2, 4, 2, 0, 2, 7, 4, 2, 4, 4, 4, 0, 0, 7, 6, 5, 1, 1, 5, 6, 1, 5, 2, 0, 0, 9, 3, 5, 2, 0, 7, 4, 8, 5, 0, 3, 2, 1, 8, 3, 6, 5, 1, 9, 5, 4, 5, 1, 3, 4, 2, 4, 6, 5, 9, 5
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OFFSET

0,1


COMMENTS

A root of r^4 + 2 r^2  1 = 0.
Also real part of sqrt(1 + i)^3, where i is the imaginary unit such that i^2 = 1.  Alonso del Arte, Sep 09 2019


REFERENCES

C. L. Siegel, Topics in Complex Function Theory, Volume I: Elliptic Functions and Uniformization Theory, WileyInterscience, 1969, page 5


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000


EXAMPLE

0.643594252905582624735443437418...


MATHEMATICA

nmax = 1000; First[ RealDigits[ Sqrt[Sqrt[2]  1], 10, nmax] ]


PROG

(PARI) sqrt(sqrt(2)  1) \\ Michel Marcus, Dec 10 2016


CROSSREFS

Cf. A154739 for the abscissa and A154743 for the ordinate.
Cf. A154748, A154749 and A154750 for the continued fraction and the numerators and denominators of the convergents.
Cf. A085565 for 1.311028777..., the firstquadrant arc length of the unit lemniscate.
Cf. A309948 and A309949 for real and imaginary parts of sqrt(1 + i).
Sequence in context: A235509 A224927 A200104 * A217515 A079624 A035335
Adjacent sequences: A154744 A154745 A154746 * A154748 A154749 A154750


KEYWORD

nonn,cons,easy


AUTHOR

Stuart Clary, Jan 14 2009


EXTENSIONS

Offset corrected by R. J. Mathar, Feb 05 2009


STATUS

approved



